Shorting is to win money in a bear market.
It's done by borrowing BTC when price is high and selling them at this price.
Once the price dropped enough for you, you buy back the same numbers of BTC, but for a lower price. You give them back to the owner (+ a fee), and keep the difference.

In practice this is all automatized and you only have to click on the short/sell button. It is usually done with leverage, so be careful.

You can short at bitfinex, wex, and poloniex.